Among them was the need for a new federal bureau to compile better data on demographics and labor markets, and brief Congress on that data.

"We agree that a professional bureau in a federal executive agency, with political independence analogous to the Bureau of Labor Statistics, should be established to inform Congress and the public about these issues," reads the joint statement by U.S. Chamber of Commerce President Thomas Donahue and AFL-CIO President Richard Trumka.

The existence of such a federal body would facilitate giving out new visas for low-skilled workers based on labor needs. It's a proposal long supported by D.C.-based think tanks for all levels of workers.

"The idea that we have been promoting together for many years, of a commission or a bureau of experts in economics and demography that would help determine the flows, the future flows of immigrant and non-immigrant workers, is now at the heart of the comprehensive immigration reform debate on Capitol Hill," said Ross Eisenbray, the vice president of the Economic Policy Institute.

Such a body would likely make recommendations to Congress but would not have regulatory authority.

Eisenbray said he expected the proposal would wind up in the blueprint being drafted by the so-called Gang of Eight bipartisan senators who are leading the immigration effort in the Senate.

"The fact that the business community and the labor community have come to agree on the importance of having an executive agency, I think is a very important step forward," Meisner said.

She also said "there are a number of precedents that already exist" for such a bureau.

Meanwhile, the topic of immigrant labor will continue to be debate in congressional hearing this week.

The House Committee on the Judiciary will hold hearings on agricultural labor on Tuesday, and another on E-Verify, a database that allows employers to check the immigration status of their workers, on Wednesday.